Measuring Conceptual Understanding, Procedural Fluency and Integrating Procedural and Conceptual Knowledge in Mathematical Problem Solving

The main aim of this paper is to meassure students’ mathematical proficiency on conceptual understanding and procedural fluency, and their ability of integrating procedural and conceptual knowledge in problem solving. Based on the PCK taxonomy (Ho 2018), we design a questionnaire consisting of 12 questions with 22 tasks whose content is focus on linear functions and equations. The collected data is analysed by the statistical software IBM SPSS Statistics 22. Moreover, we use the structural equation modeling (SEM) to study the correlation between these two components of mathematical proficiency and the ability of integrating procedural and conceptual knowledge in problem solving, implemented in IBM SPSS AMOS 24. The findings show that students’ mathematical proficiency on procedural fluency on linear functions and equations is higher than that of conceptual understanding, and their ability of integrating procedural and conceptual knowledge is very low. Moreover, these categories have a bi-directional relationship, in which the affection of mathematical proficiency on conceptual understanding to the ability of integrating procedural and conceptual knowledge in problem solving is stronger than on procedural fluency.